Numerical Methods 1100-1ENMETNUM3

Numerical analysis, or numerical methods of solving mathematical problems, is probably as old as mathematics itself. The oldest known algorithms are dated 1800 BC, many more come from ancient Greece, and another group, named by their creators (Newton, Gauss, Euler, Lagrange) suggest outburst in XVIII century. With beginning of era of computers, the numerical methods are the basic methods of problem solving in all practical applications, from physics to social sciences, from engineering to medicine.

Regardless of programming language, sophisticated libraries, graphical programs, every person using computer for numerical calculations. should be aware of certain limitations. Some of them come from the mathematical construction of the algorithm itself, but other are deeply bounded to the way the computers are performing floating point calculations. Lack of knowledge in that matter may result in some circumstances in a tragic situations (literally).

Program:
1. How computers perform numerical calculations? What problems arises from this?
2. How do we construct algorithms? How to take care of their convergence and stability?
3. How to solve any equation, even such without analytical solution?
4. How to sort a deck of cards? How to fast sort a database of population?
5. How to find what was result of experiment, between known data points?
6. How to calculate differential and integral of any function?
7. Why physicist talk a lot about Monte Carlo?
8. How do the bacteria grow? How the population of rabbits and foxes change? Why it is difficult to restart nuclear reactor?

The lecture will be accompanied by classes where students will write programs implementing and testing the algorithms. We will use two optional programming languages: C++ (with gnuplot for data visualization) and Python (with matplotlib).

The final grade will depend on test (25%), and notes given by assistants for class activities (75%).